Almost several decades after the discovery of the first multiple populations in galactic globular clusters (GC), the debate on their formation is still extremely current and NGC 2808 remains one of the best benchmark to test any scenario for their origin and the evolution. In this work, we focus on the chemical composition of stars belonging to the extreme He-rich population populated by stars with the most extreme abundance of Mg, Al, Na, O, and Si. We checked whether the most recent measures are consistent with the asymptotic giant branch (AGB) yields of stars of 6.5-8 M_{⊙}. These stars evolve on time scales of the order of 40-60 Myr and eject matter strongly enriched in helium, owing to a deep penetration of the surface convective zone down to regions touched by CNO nucleosynthesis occurring after the core He-burning phase. Since the big unknown of the AGB phase of massive stars is the mass-loss, we propose a new approch that takes into account the effects of the radiation pressure on dust particles. We show that this more realistic description is able to reproduce the observed abundances of Mg, Al, Na, and Si in these extreme stars. The large spread in the oxygen abundances is explained by invoking deep mixing during the red giant branch phase. It will be possible to check this work hypothesis as soon as the oxygen measurements of the main-sequence stars of NGC 2808 will be available.